Finite Group Databasebeta

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C₄₇×#470 #15688725

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49)(50,51)(52,53,56,59)(54,60,62,67)(55,64,61,58)(57,65,66,63);(52,54,61,65,56,62,55,63)(53,57,64,67,59,66,58,60);(49,51)(54,62)(57,66)(60,67)(63,65)

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 151);